Vibrations of Linear Piezostructures
5. Linear Piezoelectricity
Linear piezoelectric materials transform electrical energy into mechanical energy, and vice versa, in a process that is lossless and reversible. This chapter derives the equations that govern linear piezoelectric materials in three dimensions by synthesizing results from continuum mechanics in Chapter 3 and continuum electrodynamics in Chapter 4. Simple physical experiments described in Section 5.1 illustrate how the piezoelectric effect manifests in one spatial dimension. Section 5.1 introduces the constitutive laws of linear piezoelectricity and shows how they can be interpreted as an extension of the Generalized Hooke’s Law of linear elasticity. The rigorous foundations and assumptions that underly the theory of linear piezoelectricity are presented in Section 5.2. The initial-boundary value problem of linear piezoelectricity introduced in Section 5.2 is shown to be a generalization of the initial-boundary value problem of linear elasticity. Section 5.3 explores the diverse forms that the constitutive laws of linear piezoelectricity can take by using arguments based on thermodynamics.